The "invisible mode" configurations are characterized by much longer distance from the creation zone to the end of veto, as can be seen
in Table REF . However, for small values of \(\epsilon \)  this is not a problem as the particle \(a\)  is relatively long-lived.
There is a significant probability that after
its creation in the ECAL and passing the first HCAL1 module serving as a shield/veto it would be observed in the NA64 detector in one of
the two signatures: (S1) as an event with \(a \rightarrow e^+e^-\)  decay inside the HCAL2 or HCAL3 modules (HCAL2,3 in the following), or (S2) as an event
with a significant missing energy if it decays beyond HCAL2,3.
In both cases the main requirements were that the
shower profile in ECAL is compatible with electron, the VETO counter signal is smaller than 0.9 \(MIP\)  and that the energy deposition
in HCAL1 is smaller than 1 GeV. The main requirements for the signature (S1) event were that the total energy deposition in HCAL \(E_{HCAL}\gtrsim 15\)  GeV,
and that the energy deposited in HCAL2,3 is concentrated in the central cell [1]}. For the signature (S2) the total
energy deposition in ECAL was required to be smaller than 50 GeV and the energy in all HCAL modules should be smaller than 1 GeV.
There was also a number of other criteria explained in more details for the signature (S1) in [1]} and
for the signature (S2) in [3]}, [4]}.
